A Treatise on Plane and Spherical Trigonometry: And Its Applications to Astronomy and Geodesy with Numerous ExamplesD.C. Heath & Company, 1892 - 368 páginas |
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Página iii
... solution of triangles . It is hoped that the work may commend itself , not only to those who wish to confine themselves to the numerical calculations which occur in Trigonometry , but also to those who intend to pursue the study of the ...
... solution of triangles . It is hoped that the work may commend itself , not only to those who wish to confine themselves to the numerical calculations which occur in Trigonometry , but also to those who intend to pursue the study of the ...
Página vii
... is Given 112 112 114 80. To find the Angle whose Logarithmic Cosine is Given . 81. Angles near the Limits of the Quadrant Examples . 115 116 117 CHAPTER V. SOLUTION OF TRIGONOMETRIC EQUATIONS . ᎪᎡᎢ . 82. CONTENTS . vii.
... is Given 112 112 114 80. To find the Angle whose Logarithmic Cosine is Given . 81. Angles near the Limits of the Quadrant Examples . 115 116 117 CHAPTER V. SOLUTION OF TRIGONOMETRIC EQUATIONS . ᎪᎡᎢ . 82. CONTENTS . vii.
Página viii
... SOLUTION OF TRIGONOMETRIC EQUATIONS . ᎪᎡᎢ . 82. Trigonometric Equations .... 83. To solve m sin pa , m cos = b .. 84. To solve a sin + b cos = c .. 85. To solve sin ( α + x ) = m sin x . 86. To solve tan ( α + x ) : = m tan x . 87 ...
... SOLUTION OF TRIGONOMETRIC EQUATIONS . ᎪᎡᎢ . 82. Trigonometric Equations .... 83. To solve m sin pa , m cos = b .. 84. To solve a sin + b cos = c .. 85. To solve sin ( α + x ) = m sin x . 86. To solve tan ( α + x ) : = m tan x . 87 ...
Página xi
... Solution 274 189. Quadrantal Triangles 274 190. Law of Sines 191. Law of Cosines .. 276 .. 277 192. Relation between ... SOLUTION OF SPHERICAL TRIANGLES . 199. Preliminary Observations 297 200. Solution of Right Spherical Triangles . 297 ...
... Solution 274 189. Quadrantal Triangles 274 190. Law of Sines 191. Law of Cosines .. 276 .. 277 192. Relation between ... SOLUTION OF SPHERICAL TRIANGLES . 199. Preliminary Observations 297 200. Solution of Right Spherical Triangles . 297 ...
Página xii
... Solution of Oblique Spherical Triangles . 209. Case I.- Given Two Sides and the Included Angle . Given Two Angles and the Included Side .. 210. Case II . - 211. Case III .. - Given Two Sides and One Opposite Angle ... Given Two Angles ...
... Solution of Oblique Spherical Triangles . 209. Case I.- Given Two Sides and the Included Angle . Given Two Angles and the Included Side .. 210. Case II . - 211. Case III .. - Given Two Sides and One Opposite Angle ... Given Two Angles ...
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Otras ediciones - Ver todas
A Treatise on Plane and Spherical Trigonometry: And Its Applications to ... Edward Albert Bowser Sin vista previa disponible - 2013 |
Términos y frases comunes
algebraically angle AOP angle of elevation base calculate centre circle circular measure common logarithms cos b cos cos² cosec cotangent decimal places denote diff equal equations EXAMPLES expression feet find log find the angle find the height find the number formulæ Given log Hence horizon hypotenuse integer log cot log sin log sine mantissa Multiply negative number whose logarithm observed obtained opposite perpendicular plane polar triangle positive Prove the following quadrant R₁ r₂ radian radius right angles right triangle sec² secant sides Similarly sin a cos sin B sin sin x sin² sin³ sines and cosines sinx siny solution Solve spherical triangle subtends table of logarithms table of natural tan² tangent triangle ABC trigonometric functions vertical yards ОР
Pasajes populares
Página 148 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.
Página 147 - Law of Sines. — In any triangle the sides are proportional to the sines of the opposite angles.
Página 278 - AB'C, we have by (4) cos a' — cos b cos c' + sin b sin c' cos B'AC, or cos(тг— a) = cos b cos(тг— c) + sin b sin(тт — C)COS(тг —A). .-. cos a = cos b cos с + sin b sin с cos A.
Página 278 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.
Página 278 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Página 6 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Página 17 - If the cosine of A be subtracted from unity, the remainder is called the versed sine of A. If the sine of A be...
Página 89 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 149 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.